Abstract

Detecting nonclassical properties that do not allow classical interpretation of photoelectric counting events is one of the crucial themes in quantum optics. Observation of individual nonclassical effects for a single-mode field, however, has been so far practically confined to sub-Poissonian statistics and quadrature squeezing. We show that a photon-added classical (coherent or thermal) state exhibits generalized nonclassical features in all orders of creation and annihilation operators, thereby becoming a promising candidate for studying higher-order nonclassical effects. Our analysis demonstrates the robustness of these effects against nonideal experimental conditions.

© 2009 Optical Society of America

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  1. R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529-2539 (1963).
    [Crossref]
  2. R. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766-2788 (1963).
    [Crossref]
  3. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277-279 (1963).
    [Crossref]
  4. L. Mandel, “Nonclassical states of the electromagnetic. field,” Phys. Scr. T12, 34-42 (1986).
    [Crossref]
  5. U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).
  6. H. J. Carmichael and D. F. Walls, “A quantum-mechanical master equation treatment of the dynamical Stark effect,” J. Phys. B 9, 1199-1219 (1976).
    [Crossref]
  7. H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691-695 (1977).
    [Crossref]
  8. R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384-387 (1977).
    [Crossref]
  9. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
    [Crossref] [PubMed]
  10. P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316-A334 (1964).
    [Crossref]
  11. C. K. Hong and L. Mandel, “Higher-order squeezing of a quantum field,” Phys. Rev. Lett. 54, 323-325 (1985).
    [Crossref] [PubMed]
  12. M. Hillery, “Amplitude-squared squeezing of the electromagnetic field,” Phys. Rev. A 36, 3796-3802 (1987).
    [Crossref] [PubMed]
  13. C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721-1723 (1990).
    [Crossref] [PubMed]
  14. G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
    [Crossref] [PubMed]
  15. E. Shchukin, Th. Richter, and W. Vogel, “Nonclassicality criteria in terms of moments,” Phys. Rev. A 71, 011802 (2005).
    [Crossref]
  16. J. K. Asboth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett. 94, 173602 (2005).
    [Crossref] [PubMed]
  17. H. Nha and M. S. Zubairy, “Uncertainty inequalities as entanglement criteria for negative partial-transpose states,” Phys. Rev. Lett. 101, 130402 (2008).
    [Crossref] [PubMed]
  18. Z.-M. Zhang, L. Xu, J.-L. Chai, and F.-L. Li, “A new kind of higher-order squeezing of radiation field,” Phys. Lett. A 150, 27-30 (1990).
    [Crossref]
  19. G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
    [Crossref] [PubMed]
  20. M. Dakna, L. Knöll, and D.-G. Welsch, “Photon-added state preparation via conditional measurement on a beam splitter,” Opt. Commun. 145, 309-321 (1998).
    [Crossref]
  21. M. Dakna, L. Knöll, and D.-G. Welsch, “Quantum state engineering using conditional measurement on a beam splitter,” Eur. Phys. J. D 3, 295-308 (1998).
    [Crossref]
  22. A. R. Usha Devi, R. Prabhu, and M. S. Uma, “Nonclassicality of photon added coherent and thermal radiations,” Eur. Phys. J. D 40, 133-138 (2006).
    [Crossref]
  23. A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
    [Crossref] [PubMed]
  24. A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
    [Crossref]
  25. A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
    [Crossref]
  26. V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
    [Crossref] [PubMed]
  27. T. M. Duc and J. Noh, “Higher-order properties of photon-added coherent states,” Opt. Commun. 281, 2842-2848 (2008).
    [Crossref]
  28. A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
    [Crossref] [PubMed]
  29. A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett. 88, 250401 (2002).
    [Crossref] [PubMed]
  30. S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
    [Crossref] [PubMed]
  31. E. Shchukin and W. Vogel, “Universal measurement of quantum correlations of radiation,” Phys. Rev. Lett. 96, 200403 (2006).
    [Crossref] [PubMed]

2008 (2)

H. Nha and M. S. Zubairy, “Uncertainty inequalities as entanglement criteria for negative partial-transpose states,” Phys. Rev. Lett. 101, 130402 (2008).
[Crossref] [PubMed]

T. M. Duc and J. Noh, “Higher-order properties of photon-added coherent states,” Opt. Commun. 281, 2842-2848 (2008).
[Crossref]

2007 (2)

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[Crossref] [PubMed]

2006 (2)

A. R. Usha Devi, R. Prabhu, and M. S. Uma, “Nonclassicality of photon added coherent and thermal radiations,” Eur. Phys. J. D 40, 133-138 (2006).
[Crossref]

E. Shchukin and W. Vogel, “Universal measurement of quantum correlations of radiation,” Phys. Rev. Lett. 96, 200403 (2006).
[Crossref] [PubMed]

2005 (3)

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[Crossref]

E. Shchukin, Th. Richter, and W. Vogel, “Nonclassicality criteria in terms of moments,” Phys. Rev. A 71, 011802 (2005).
[Crossref]

J. K. Asboth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett. 94, 173602 (2005).
[Crossref] [PubMed]

2004 (2)

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[Crossref] [PubMed]

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

2002 (1)

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett. 88, 250401 (2002).
[Crossref] [PubMed]

2001 (1)

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

1998 (2)

M. Dakna, L. Knöll, and D.-G. Welsch, “Photon-added state preparation via conditional measurement on a beam splitter,” Opt. Commun. 145, 309-321 (1998).
[Crossref]

M. Dakna, L. Knöll, and D.-G. Welsch, “Quantum state engineering using conditional measurement on a beam splitter,” Eur. Phys. J. D 3, 295-308 (1998).
[Crossref]

1992 (1)

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[Crossref] [PubMed]

1991 (1)

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[Crossref] [PubMed]

1990 (2)

C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721-1723 (1990).
[Crossref] [PubMed]

Z.-M. Zhang, L. Xu, J.-L. Chai, and F.-L. Li, “A new kind of higher-order squeezing of radiation field,” Phys. Lett. A 150, 27-30 (1990).
[Crossref]

1987 (1)

M. Hillery, “Amplitude-squared squeezing of the electromagnetic field,” Phys. Rev. A 36, 3796-3802 (1987).
[Crossref] [PubMed]

1986 (1)

L. Mandel, “Nonclassical states of the electromagnetic. field,” Phys. Scr. T12, 34-42 (1986).
[Crossref]

1985 (2)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
[Crossref] [PubMed]

C. K. Hong and L. Mandel, “Higher-order squeezing of a quantum field,” Phys. Rev. Lett. 54, 323-325 (1985).
[Crossref] [PubMed]

1977 (2)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691-695 (1977).
[Crossref]

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384-387 (1977).
[Crossref]

1976 (1)

H. J. Carmichael and D. F. Walls, “A quantum-mechanical master equation treatment of the dynamical Stark effect,” J. Phys. B 9, 1199-1219 (1976).
[Crossref]

1964 (1)

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316-A334 (1964).
[Crossref]

1963 (3)

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529-2539 (1963).
[Crossref]

R. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766-2788 (1963).
[Crossref]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277-279 (1963).
[Crossref]

Agarwal, G. S.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[Crossref] [PubMed]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[Crossref] [PubMed]

Aichele, T.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

Asboth, J. K.

J. K. Asboth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett. 94, 173602 (2005).
[Crossref] [PubMed]

Babichev, S. A.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

Bellini, M.

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[Crossref] [PubMed]

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[Crossref]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[Crossref] [PubMed]

Benson, O.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

Brezger, B.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

Calsamiglia, J.

J. K. Asboth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett. 94, 173602 (2005).
[Crossref] [PubMed]

Carmichael, H. J.

H. J. Carmichael and D. F. Walls, “A quantum-mechanical master equation treatment of the dynamical Stark effect,” J. Phys. B 9, 1199-1219 (1976).
[Crossref]

Chai, J. -L.

Z.-M. Zhang, L. Xu, J.-L. Chai, and F.-L. Li, “A new kind of higher-order squeezing of radiation field,” Phys. Lett. A 150, 27-30 (1990).
[Crossref]

Dagenais, M.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691-695 (1977).
[Crossref]

Dakna, M.

M. Dakna, L. Knöll, and D.-G. Welsch, “Photon-added state preparation via conditional measurement on a beam splitter,” Opt. Commun. 145, 309-321 (1998).
[Crossref]

M. Dakna, L. Knöll, and D.-G. Welsch, “Quantum state engineering using conditional measurement on a beam splitter,” Eur. Phys. J. D 3, 295-308 (1998).
[Crossref]

Duc, T. M.

T. M. Duc and J. Noh, “Higher-order properties of photon-added coherent states,” Opt. Commun. 281, 2842-2848 (2008).
[Crossref]

Glauber, R.

R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529-2539 (1963).
[Crossref]

R. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766-2788 (1963).
[Crossref]

Hansen, H.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

Hillery, M.

M. Hillery, “Amplitude-squared squeezing of the electromagnetic field,” Phys. Rev. A 36, 3796-3802 (1987).
[Crossref] [PubMed]

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
[Crossref] [PubMed]

Hong, C. K.

C. K. Hong and L. Mandel, “Higher-order squeezing of a quantum field,” Phys. Rev. Lett. 54, 323-325 (1985).
[Crossref] [PubMed]

Kelley, P. L.

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316-A334 (1964).
[Crossref]

Kim, M.

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[Crossref] [PubMed]

Kimble, H. J.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691-695 (1977).
[Crossref]

Kleiner, W. H.

P. L. Kelley and W. H. Kleiner, “Theory of electromagnetic field measurement and photoelectron counting,” Phys. Rev. 136, A316-A334 (1964).
[Crossref]

Knöll, L.

M. Dakna, L. Knöll, and D.-G. Welsch, “Quantum state engineering using conditional measurement on a beam splitter,” Eur. Phys. J. D 3, 295-308 (1998).
[Crossref]

M. Dakna, L. Knöll, and D.-G. Welsch, “Photon-added state preparation via conditional measurement on a beam splitter,” Opt. Commun. 145, 309-321 (1998).
[Crossref]

Lee, C. T.

C. T. Lee, “Higher-order criteria for nonclassical effects in photon statistics,” Phys. Rev. A 41, 1721-1723 (1990).
[Crossref] [PubMed]

Leonhardt, U.

U. Leonhardt, Measuring the Quantum State of Light (Cambridge U. Press, 1997).

Li, F. -L.

Z.-M. Zhang, L. Xu, J.-L. Chai, and F.-L. Li, “A new kind of higher-order squeezing of radiation field,” Phys. Lett. A 150, 27-30 (1990).
[Crossref]

Lvovsky, A. I.

S. A. Babichev, B. Brezger, and A. I. Lvovsky, “Remote preparation of a single-mode photonic qubit by measuring field quadrature noise,” Phys. Rev. Lett. 92, 047903 (2004).
[Crossref] [PubMed]

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett. 88, 250401 (2002).
[Crossref] [PubMed]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

Mandel, L.

L. Mandel, “Nonclassical states of the electromagnetic. field,” Phys. Scr. T12, 34-42 (1986).
[Crossref]

C. K. Hong and L. Mandel, “Higher-order squeezing of a quantum field,” Phys. Rev. Lett. 54, 323-325 (1985).
[Crossref] [PubMed]

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691-695 (1977).
[Crossref]

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384-387 (1977).
[Crossref]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
[Crossref] [PubMed]

Mlynek, J.

A. I. Lvovsky and J. Mlynek, “Quantum-optical catalysis: generating nonclassical states of light by means of linear optics,” Phys. Rev. Lett. 88, 250401 (2002).
[Crossref] [PubMed]

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

Nha, H.

H. Nha and M. S. Zubairy, “Uncertainty inequalities as entanglement criteria for negative partial-transpose states,” Phys. Rev. Lett. 101, 130402 (2008).
[Crossref] [PubMed]

Noh, J.

T. M. Duc and J. Noh, “Higher-order properties of photon-added coherent states,” Opt. Commun. 281, 2842-2848 (2008).
[Crossref]

Parigi, V.

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[Crossref] [PubMed]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

Prabhu, R.

A. R. Usha Devi, R. Prabhu, and M. S. Uma, “Nonclassicality of photon added coherent and thermal radiations,” Eur. Phys. J. D 40, 133-138 (2006).
[Crossref]

Richter, Th.

E. Shchukin, Th. Richter, and W. Vogel, “Nonclassicality criteria in terms of moments,” Phys. Rev. A 71, 011802 (2005).
[Crossref]

Ritsch, H.

J. K. Asboth, J. Calsamiglia, and H. Ritsch, “Computable measure of nonclassicality for light,” Phys. Rev. Lett. 94, 173602 (2005).
[Crossref] [PubMed]

Schiller, S.

A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon Fock state,” Phys. Rev. Lett. 87, 050402 (2001).
[Crossref] [PubMed]

Shchukin, E.

E. Shchukin and W. Vogel, “Universal measurement of quantum correlations of radiation,” Phys. Rev. Lett. 96, 200403 (2006).
[Crossref] [PubMed]

E. Shchukin, Th. Richter, and W. Vogel, “Nonclassicality criteria in terms of moments,” Phys. Rev. A 71, 011802 (2005).
[Crossref]

Short, R.

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384-387 (1977).
[Crossref]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
[Crossref] [PubMed]

Sudarshan, E. C. G.

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277-279 (1963).
[Crossref]

Tara, K.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485-488 (1992).
[Crossref] [PubMed]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492-497 (1991).
[Crossref] [PubMed]

Uma, M. S.

A. R. Usha Devi, R. Prabhu, and M. S. Uma, “Nonclassicality of photon added coherent and thermal radiations,” Eur. Phys. J. D 40, 133-138 (2006).
[Crossref]

Usha Devi, A. R.

A. R. Usha Devi, R. Prabhu, and M. S. Uma, “Nonclassicality of photon added coherent and thermal radiations,” Eur. Phys. J. D 40, 133-138 (2006).
[Crossref]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
[Crossref] [PubMed]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[Crossref]

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660-662 (2004).
[Crossref] [PubMed]

Vogel, W.

E. Shchukin and W. Vogel, “Universal measurement of quantum correlations of radiation,” Phys. Rev. Lett. 96, 200403 (2006).
[Crossref] [PubMed]

E. Shchukin, Th. Richter, and W. Vogel, “Nonclassicality criteria in terms of moments,” Phys. Rev. A 71, 011802 (2005).
[Crossref]

Walls, D. F.

H. J. Carmichael and D. F. Walls, “A quantum-mechanical master equation treatment of the dynamical Stark effect,” J. Phys. B 9, 1199-1219 (1976).
[Crossref]

Welsch, D. -G.

M. Dakna, L. Knöll, and D.-G. Welsch, “Photon-added state preparation via conditional measurement on a beam splitter,” Opt. Commun. 145, 309-321 (1998).
[Crossref]

M. Dakna, L. Knöll, and D.-G. Welsch, “Quantum state engineering using conditional measurement on a beam splitter,” Eur. Phys. J. D 3, 295-308 (1998).
[Crossref]

Xu, L.

Z.-M. Zhang, L. Xu, J.-L. Chai, and F.-L. Li, “A new kind of higher-order squeezing of radiation field,” Phys. Lett. A 150, 27-30 (1990).
[Crossref]

Yurke, B.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409-2412 (1985).
[Crossref] [PubMed]

Zavatta, A.

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[Crossref]

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890-1893 (2007).
[Crossref] [PubMed]

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Experimental schemes to implement single-photon-added states using (a) beam splitter and (b) NDPA. ρ in is the input state, ρ single is the single-photon source, and ρ c is the output state conditioned on the detection of (a) no photon and (b) single photon. a s : signal mode, a i : idler mode, BS: beam splitter, PD: photodetector.

Fig. 2
Fig. 2

Contour plot for the probability P ND to generate an approximate SACS conditioned on the nondetection of photons as a function of α and R = sin 2 θ (reflectance of the beam splitter) for (a) η = 1 and p S = 1 , and (b) for η = 0.6 and p S = 0.7 .

Fig. 3
Fig. 3

Contour plot of Q 1 m of SACS as a function of α and R = sin 2 θ for (a), (b) m = 1 (quadrature squeezing), (c), (d) m = 2 (Hillery’s amplitude squared squeezing [12]), and (e), (f) m = 3 . The left-column plots [(a), (c), and (e)] are for the ideal case of η = 1 and p S = 1 , and the right-column ones [(b), (d), and (f)] are for η = 0.6 and p S = 0.7 . The dashed curves ( Q 1 m = 0 ) represent the boundary between classical and nonclassical regimes.

Fig. 4
Fig. 4

Contour plot of Q 2 m = 4 of SACS as a function of α and R = sin 2 θ for (a) η = 1 and p S = 1 , and (b) η = 0.6 and p S = 0.7 . The dashed curves ( Q 2 m = 0 ) represents the boundary between classical and nonclassical regimes.

Fig. 5
Fig. 5

The probability P ND to generate an approximate SATS conditioned on the nondetection of photons as a function of 1 / n ¯ and R = sin 2 θ for (a) η = 1 and p S = 1 , and (b) η = 0.6 and p S = 0.7 .

Fig. 6
Fig. 6

Contour plot of Q 2 m of SATS as a function of 1 / n ¯ and R = sin 2 θ for (a), (b) m = 1 (sub-Poissonian statistics), (c), (d) m = 2 , and (e), (f) m = 3 . The left-column plots [(a), (c), and (e)] are for the ideal case of η = 1 and p S = 1 , and the right-column ones [(b), (d), and (f)] are for η = 0.6 and p S = 0.7 .

Fig. 7
Fig. 7

Plot of Q 1 m as a function of α and η for (a), (b) m = 2 (Hillery’s amplitude squared squeezing [12]) and (c), (d) m = 3 in the NDPA scheme. The dashed lines represent the boundary ( Q 1 m = 0 ) between classical and nonclassical regimes. In (a) and (c), the dotted line corresponds to η = 0.62 for which Q 1 m is plotted again as a function of α in (b) and (d), respectively.

Equations (29)

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: f ̂ 1 f ̂ 1 : = : ( Δ ( a m e i ϕ + a m e i ϕ ) ) 2 : < 0 ,
( Δ ( a m e i ϕ + a m e i ϕ ) ) 2 = : ( Δ ( a m e i ϕ + a m e i ϕ ) ) 2 : + [ a m , a m ] .
Q 1 m ( ϕ ) = : ( Δ ( a m e i ϕ + a m e i ϕ ) ) 2 : a m a m a m a m ,
: ( Δ ( a m e i ϕ + a m e i ϕ ) ) 2 : = ζ e 2 i ϕ + ζ e 2 i ϕ + 2 a m a m 2 a m a m ,
ζ a 2 m a m 2 .
Q 1 m = 2 | a 2 m a m 2 | + 2 a m a m 2 | a m | 2 a m a m a m a m ,
: f ̂ 2 f ̂ 2 : = : ( Δ ( a m a m ) 2 ) : = a 2 m a 2 m a m a m 2 < 0.
Q 2 m = a 2 m a 2 m a m a m 2 1 ,
a m SACS = α m 1 + α 2 ( m + 1 + α 2 ) ,
a m a m SACS = α 2 m + 2 + ( 2 m + 1 ) α 2 m + m 2 α 2 m 2 1 + α 2 .
| a 2 m a m 2 | + a m a m | a m | 2 = m 2 α 2 m 2 ( 1 + α 2 ) 2 ( α 2 1 ) ,
Q 2 m = α 2 ( 1 + α 2 ) α 4 + ( 4 m + 1 ) α 2 + 4 m 2 ( α 4 + ( 2 m + 1 ) α 2 + m 2 ) 2 1 < 0 ,
a m a m SATS = m ! x m ( 1 + m ( 1 + x ) ) ,
Q 2 m = ( 2 m ) ! ( m ! ) 2 2 m ( 1 + x ) + 1 ( m ( 1 + x ) + 1 ) 2 1 < 0 ,
x > C m ( 2 m ) ! ( m ! ) 2 + ( 2 m ) ! ( ( 2 m ) ! ( m ! ) 2 ) m ( m ! ) 2 .
( b 1 b 2 ) = B 12 ( a 1 a 2 ) B 12 = ( cos   θ sin   θ sin   θ cos   θ ) ( a 1 a 2 ) ,
ρ c = 1 P ND Tr 2 { Π 2 0 B 12 ρ in ρ single B 12 } ,
P ND = Tr 1 , 2 { Π 2 0 B 12 ρ in ρ single B 12 } .
ρ c = 1 N [ s a | β β | a + f | β β | + c | β β | a + c a | β β | ] ,
s R p S ,
f p S ( 1 η ) T ( 1 + ( 1 η ) R α 2 ) + ( 1 p S ) ,
c R p S ( 1 η ) β ,
N p S ( 1 T η + R T η 2 α 2 ) + 1 p S ,
P ND = N e R η α 2 .
a m = 1 N [ s β m ( β 2 + m + 1 ) + f β m + c β m 1 ( 2 β 2 + m ) ] ,
a m a m = 1 N [ s β 2 m 2 ( ( β 2 + m ) 2 + β 2 ) + f β 2 m + 2 c β 2 m 1 ( β 2 + m ) ] .
a m a m = p = 0 m ( m ! ) 2 ( m p ) ! ( p ! ) 2 a p a p .
a 1 m a 1 m = Tr 1 { a 1 m a 1 m ρ c } = Tr 1 , 2 { a 1 m a 1 m Π 2 0 B 12 ρ in ρ single B 12 } Tr 1 , 2 { Π 2 0 B 12 ρ in ρ single B 12 } D m D 0 ,
D m = m ! T m 1 n ¯ 1 ( n ¯ 1 + η R ) m + 2 [ T ( n ¯ 1 + η R ) ( 1 η p S T + 2 m η p S R ) + m p S R ( n ¯ 1 + η R ) 2 + ( m + 1 ) η 2 p S R T 2 ] ,

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